LMFDB - Embedded newform 4598.2.a.ca.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4598,2,Mod(1,4598)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4598, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4598.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4598 = 2 \cdot 11^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4598.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$36.7152148494$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 10x^{6} + 16x^{5} + 26x^{4} - 32x^{3} - 16x^{2} + 20x - 4 $ x^8 - 2x^7 - 10x^6 + 16x^5 + 26x^4 - 32x^3 - 16x^2 + 20*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.03422$ of defining polynomial
Character	$\chi$	$=$	4598.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.912987 q^{3} +1.00000 q^{4} -1.77724 q^{5} +0.912987 q^{6} -5.04753 q^{7} +1.00000 q^{8} -2.16645 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.912987 q^{3} +1.00000 q^{4} -1.77724 q^{5} +0.912987 q^{6} -5.04753 q^{7} +1.00000 q^{8} -2.16645 q^{9} -1.77724 q^{10} +0.912987 q^{12} +5.42371 q^{13} -5.04753 q^{14} -1.62260 q^{15} +1.00000 q^{16} -1.82249 q^{17} -2.16645 q^{18} -1.00000 q^{19} -1.77724 q^{20} -4.60833 q^{21} +5.61764 q^{23} +0.912987 q^{24} -1.84141 q^{25} +5.42371 q^{26} -4.71691 q^{27} -5.04753 q^{28} +2.23982 q^{29} -1.62260 q^{30} +0.386531 q^{31} +1.00000 q^{32} -1.82249 q^{34} +8.97068 q^{35} -2.16645 q^{36} -10.0927 q^{37} -1.00000 q^{38} +4.95177 q^{39} -1.77724 q^{40} +9.28332 q^{41} -4.60833 q^{42} +5.45957 q^{43} +3.85031 q^{45} +5.61764 q^{46} +10.8132 q^{47} +0.912987 q^{48} +18.4776 q^{49} -1.84141 q^{50} -1.66391 q^{51} +5.42371 q^{52} +6.85692 q^{53} -4.71691 q^{54} -5.04753 q^{56} -0.912987 q^{57} +2.23982 q^{58} +3.70481 q^{59} -1.62260 q^{60} +2.89301 q^{61} +0.386531 q^{62} +10.9352 q^{63} +1.00000 q^{64} -9.63923 q^{65} -11.5655 q^{67} -1.82249 q^{68} +5.12883 q^{69} +8.97068 q^{70} -0.872761 q^{71} -2.16645 q^{72} +9.78216 q^{73} -10.0927 q^{74} -1.68119 q^{75} -1.00000 q^{76} +4.95177 q^{78} +9.31807 q^{79} -1.77724 q^{80} +2.19288 q^{81} +9.28332 q^{82} -4.28702 q^{83} -4.60833 q^{84} +3.23901 q^{85} +5.45957 q^{86} +2.04493 q^{87} -5.60537 q^{89} +3.85031 q^{90} -27.3763 q^{91} +5.61764 q^{92} +0.352898 q^{93} +10.8132 q^{94} +1.77724 q^{95} +0.912987 q^{96} -2.90528 q^{97} +18.4776 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9	$ 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9} + 2 q^{10} + 18 q^{13} + 8 q^{14} + 10 q^{15} + 8 q^{16} + 4 q^{17} + 20 q^{18} - 8 q^{19} + 2 q^{20} + 14 q^{21} + 12 q^{23} + 18 q^{26} - 24 q^{27} + 8 q^{28} + 14 q^{29} + 10 q^{30} - 2 q^{31} + 8 q^{32} + 4 q^{34} + 40 q^{35} + 20 q^{36} - 22 q^{37} - 8 q^{38} - 4 q^{39} + 2 q^{40} + 8 q^{41} + 14 q^{42} + 28 q^{43} - 28 q^{45} + 12 q^{46} + 6 q^{47} + 32 q^{49} - 12 q^{51} + 18 q^{52} - 24 q^{53} - 24 q^{54} + 8 q^{56} + 14 q^{58} + 46 q^{59} + 10 q^{60} - 24 q^{61} - 2 q^{62} + 30 q^{63} + 8 q^{64} - 16 q^{65} - 22 q^{67} + 4 q^{68} - 38 q^{69} + 40 q^{70} + 8 q^{71} + 20 q^{72} + 16 q^{73} - 22 q^{74} + 6 q^{75} - 8 q^{76} - 4 q^{78} + 4 q^{79} + 2 q^{80} + 28 q^{81} + 8 q^{82} + 12 q^{83} + 14 q^{84} + 48 q^{85} + 28 q^{86} + 42 q^{87} - 28 q^{89} - 28 q^{90} - 12 q^{91} + 12 q^{92} + 22 q^{93} + 6 q^{94} - 2 q^{95} - 22 q^{97} + 32 q^{98}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9 + 2 * q^10 + 18 * q^13 + 8 * q^14 + 10 * q^15 + 8 * q^16 + 4 * q^17 + 20 * q^18 - 8 * q^19 + 2 * q^20 + 14 * q^21 + 12 * q^23 + 18 * q^26 - 24 * q^27 + 8 * q^28 + 14 * q^29 + 10 * q^30 - 2 * q^31 + 8 * q^32 + 4 * q^34 + 40 * q^35 + 20 * q^36 - 22 * q^37 - 8 * q^38 - 4 * q^39 + 2 * q^40 + 8 * q^41 + 14 * q^42 + 28 * q^43 - 28 * q^45 + 12 * q^46 + 6 * q^47 + 32 * q^49 - 12 * q^51 + 18 * q^52 - 24 * q^53 - 24 * q^54 + 8 * q^56 + 14 * q^58 + 46 * q^59 + 10 * q^60 - 24 * q^61 - 2 * q^62 + 30 * q^63 + 8 * q^64 - 16 * q^65 - 22 * q^67 + 4 * q^68 - 38 * q^69 + 40 * q^70 + 8 * q^71 + 20 * q^72 + 16 * q^73 - 22 * q^74 + 6 * q^75 - 8 * q^76 - 4 * q^78 + 4 * q^79 + 2 * q^80 + 28 * q^81 + 8 * q^82 + 12 * q^83 + 14 * q^84 + 48 * q^85 + 28 * q^86 + 42 * q^87 - 28 * q^89 - 28 * q^90 - 12 * q^91 + 12 * q^92 + 22 * q^93 + 6 * q^94 - 2 * q^95 - 22 * q^97 + 32 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.912987	0.527114	0.263557	−	0.964644i	$-0.415104\pi$
$3$	0.912987	0.527114	0.263557	+	0.964644i	$0.415104\pi$
$4$	1.00000	0.500000
$5$	−1.77724	−0.794806	−0.397403	−	0.917644i	$-0.630089\pi$
$5$	−1.77724	−0.794806	−0.397403	+	0.917644i	$0.630089\pi$
$6$	0.912987	0.372726
$7$	−5.04753	−1.90779	−0.953894	−	0.300145i	$-0.902965\pi$
$7$	−5.04753	−1.90779	−0.953894	+	0.300145i	$0.902965\pi$
$8$	1.00000	0.353553
$9$	−2.16645	−0.722151
$10$	−1.77724	−0.562013
$11$	0	0
$11$	0	0
$12$	0.912987	0.263557
$13$	5.42371	1.50427	0.752133	−	0.659012i	$-0.229025\pi$
$13$	5.42371	1.50427	0.752133	+	0.659012i	$0.229025\pi$
$14$	−5.04753	−1.34901
$15$	−1.62260	−0.418953
$16$	1.00000	0.250000
$17$	−1.82249	−0.442020	−0.221010	−	0.975272i	$-0.570935\pi$
$17$	−1.82249	−0.442020	−0.221010	+	0.975272i	$0.570935\pi$
$18$	−2.16645	−0.510638
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.77724	−0.397403
$21$	−4.60833	−1.00562
$22$	0	0
$23$	5.61764	1.17136	0.585679	−	0.810543i	$-0.300828\pi$
$23$	5.61764	1.17136	0.585679	+	0.810543i	$0.300828\pi$
$24$	0.912987	0.186363
$25$	−1.84141	−0.368283
$26$	5.42371	1.06368
$27$	−4.71691	−0.907769
$28$	−5.04753	−0.953894
$29$	2.23982	0.415924	0.207962	−	0.978137i	$-0.433317\pi$
$29$	2.23982	0.415924	0.207962	+	0.978137i	$0.433317\pi$
$30$	−1.62260	−0.296245
$31$	0.386531	0.0694229	0.0347115	−	0.999397i	$-0.488949\pi$
$31$	0.386531	0.0694229	0.0347115	+	0.999397i	$0.488949\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−1.82249	−0.312555
$35$	8.97068	1.51632
$36$	−2.16645	−0.361076
$37$	−10.0927	−1.65923	−0.829615	−	0.558335i	$-0.811440\pi$
$37$	−10.0927	−1.65923	−0.829615	+	0.558335i	$0.811440\pi$
$38$	−1.00000	−0.162221
$39$	4.95177	0.792919
$40$	−1.77724	−0.281006
$41$	9.28332	1.44981	0.724906	−	0.688848i	$-0.241883\pi$
$41$	9.28332	1.44981	0.724906	+	0.688848i	$0.241883\pi$
$42$	−4.60833	−0.711081
$43$	5.45957	0.832576	0.416288	−	0.909233i	$-0.363331\pi$
$43$	5.45957	0.832576	0.416288	+	0.909233i	$0.363331\pi$
$44$	0	0
$45$	3.85031	0.573970
$46$	5.61764	0.828275
$47$	10.8132	1.57727	0.788636	−	0.614860i	$-0.210787\pi$
$47$	10.8132	1.57727	0.788636	+	0.614860i	$0.210787\pi$
$48$	0.912987	0.131778
$49$	18.4776	2.63965
$50$	−1.84141	−0.260415
$51$	−1.66391	−0.232995
$52$	5.42371	0.752133
$53$	6.85692	0.941870	0.470935	−	0.882168i	$-0.343917\pi$
$53$	6.85692	0.941870	0.470935	+	0.882168i	$0.343917\pi$
$54$	−4.71691	−0.641890
$55$	0	0
$56$	−5.04753	−0.674505
$57$	−0.912987	−0.120928
$58$	2.23982	0.294103
$59$	3.70481	0.482325	0.241163	−	0.970485i	$-0.422471\pi$
$59$	3.70481	0.482325	0.241163	+	0.970485i	$0.422471\pi$
$60$	−1.62260	−0.209477
$61$	2.89301	0.370412	0.185206	−	0.982700i	$-0.440705\pi$
$61$	2.89301	0.370412	0.185206	+	0.982700i	$0.440705\pi$
$62$	0.386531	0.0490894
$63$	10.9352	1.37771
$64$	1.00000	0.125000
$65$	−9.63923	−1.19560
$66$	0	0
$67$	−11.5655	−1.41295	−0.706474	−	0.707739i	$-0.749715\pi$
$67$	−11.5655	−1.41295	−0.706474	+	0.707739i	$0.749715\pi$
$68$	−1.82249	−0.221010
$69$	5.12883	0.617439
$70$	8.97068	1.07220
$71$	−0.872761	−0.103578	−0.0517888	−	0.998658i	$-0.516492\pi$
$71$	−0.872761	−0.103578	−0.0517888	+	0.998658i	$0.516492\pi$
$72$	−2.16645	−0.255319
$73$	9.78216	1.14491	0.572457	−	0.819934i	$-0.305990\pi$
$73$	9.78216	1.14491	0.572457	+	0.819934i	$0.305990\pi$
$74$	−10.0927	−1.17325
$75$	−1.68119	−0.194127
$76$	−1.00000	−0.114708
$77$	0	0
$78$	4.95177	0.560678
$79$	9.31807	1.04836	0.524182	−	0.851606i	$-0.324371\pi$
$79$	9.31807	1.04836	0.524182	+	0.851606i	$0.324371\pi$
$80$	−1.77724	−0.198702
$81$	2.19288	0.243654
$82$	9.28332	1.02517
$83$	−4.28702	−0.470561	−0.235281	−	0.971927i	$-0.575601\pi$
$83$	−4.28702	−0.470561	−0.235281	+	0.971927i	$0.575601\pi$
$84$	−4.60833	−0.502810
$85$	3.23901	0.351320
$86$	5.45957	0.588720
$87$	2.04493	0.219239
$88$	0	0
$89$	−5.60537	−0.594169	−0.297084	−	0.954851i	$-0.596014\pi$
$89$	−5.60537	−0.594169	−0.297084	+	0.954851i	$0.596014\pi$
$90$	3.85031	0.405858
$91$	−27.3763	−2.86982
$92$	5.61764	0.585679
$93$	0.352898	0.0365938
$94$	10.8132	1.11530
$95$	1.77724	0.182341
$96$	0.912987	0.0931814
$97$	−2.90528	−0.294987	−0.147493	−	0.989063i	$-0.547121\pi$
$97$	−2.90528	−0.294987	−0.147493	+	0.989063i	$0.547121\pi$
$98$	18.4776	1.86652
$99$	0	0
$100$	−1.84141	−0.184141
$101$	−0.530731	−0.0528097	−0.0264049	−	0.999651i	$-0.508406\pi$
$101$	−0.530731	−0.0528097	−0.0264049	+	0.999651i	$0.508406\pi$
$102$	−1.66391	−0.164752
$103$	−3.63890	−0.358552	−0.179276	−	0.983799i	$-0.557376\pi$
$103$	−3.63890	−0.358552	−0.179276	+	0.983799i	$0.557376\pi$
$104$	5.42371	0.531838
$105$	8.19012	0.799273
$106$	6.85692	0.666003
$107$	8.86825	0.857326	0.428663	−	0.903464i	$-0.358985\pi$
$107$	8.86825	0.857326	0.428663	+	0.903464i	$0.358985\pi$
$108$	−4.71691	−0.453885
$109$	−2.02691	−0.194143	−0.0970716	−	0.995277i	$-0.530948\pi$
$109$	−2.02691	−0.194143	−0.0970716	+	0.995277i	$0.530948\pi$
$110$	0	0
$111$	−9.21451	−0.874603
$112$	−5.04753	−0.476947
$113$	1.61136	0.151584	0.0757919	−	0.997124i	$-0.475852\pi$
$113$	1.61136	0.151584	0.0757919	+	0.997124i	$0.475852\pi$
$114$	−0.912987	−0.0855091
$115$	−9.98389	−0.931003
$116$	2.23982	0.207962
$117$	−11.7502	−1.08631
$118$	3.70481	0.341055
$119$	9.19910	0.843280
$120$	−1.62260	−0.148122
$121$	0	0
$122$	2.89301	0.261920
$123$	8.47556	0.764215
$124$	0.386531	0.0347115
$125$	12.1588	1.08752
$126$	10.9352	0.974189
$127$	15.7073	1.39380	0.696901	−	0.717168i	$-0.254562\pi$
$127$	15.7073	1.39380	0.696901	+	0.717168i	$0.254562\pi$
$128$	1.00000	0.0883883
$129$	4.98452	0.438862
$130$	−9.63923	−0.845416
$131$	13.6488	1.19250	0.596250	−	0.802798i	$-0.296657\pi$
$131$	13.6488	1.19250	0.596250	+	0.802798i	$0.296657\pi$
$132$	0	0
$133$	5.04753	0.437676
$134$	−11.5655	−0.999105
$135$	8.38308	0.721501
$136$	−1.82249	−0.156278
$137$	−9.02937	−0.771432	−0.385716	−	0.922618i	$-0.626045\pi$
$137$	−9.02937	−0.771432	−0.385716	+	0.922618i	$0.626045\pi$
$138$	5.12883	0.436595
$139$	10.3574	0.878500	0.439250	−	0.898365i	$-0.355244\pi$
$139$	10.3574	0.878500	0.439250	+	0.898365i	$0.355244\pi$
$140$	8.97068	0.758161
$141$	9.87235	0.831402
$142$	−0.872761	−0.0732405
$143$	0	0
$144$	−2.16645	−0.180538
$145$	−3.98070	−0.330579
$146$	9.78216	0.809577
$147$	16.8698	1.39140
$148$	−10.0927	−0.829615
$149$	14.2335	1.16605	0.583026	−	0.812454i	$-0.301869\pi$
$149$	14.2335	1.16605	0.583026	+	0.812454i	$0.301869\pi$
$150$	−1.68119	−0.137268
$151$	−14.2150	−1.15680	−0.578398	−	0.815754i	$-0.696322\pi$
$151$	−14.2150	−1.15680	−0.578398	+	0.815754i	$0.696322\pi$
$152$	−1.00000	−0.0811107
$153$	3.94835	0.319205
$154$	0	0
$155$	−0.686958	−0.0551778
$156$	4.95177	0.396459
$157$	13.8523	1.10553	0.552767	−	0.833336i	$-0.313572\pi$
$157$	13.8523	1.10553	0.552767	+	0.833336i	$0.313572\pi$
$158$	9.31807	0.741306
$159$	6.26028	0.496473
$160$	−1.77724	−0.140503
$161$	−28.3552	−2.23470
$162$	2.19288	0.172289
$163$	10.9348	0.856480	0.428240	−	0.903665i	$-0.359134\pi$
$163$	10.9348	0.856480	0.428240	+	0.903665i	$0.359134\pi$
$164$	9.28332	0.724906
$165$	0	0
$166$	−4.28702	−0.332737
$167$	3.90441	0.302132	0.151066	−	0.988524i	$-0.451729\pi$
$167$	3.90441	0.302132	0.151066	+	0.988524i	$0.451729\pi$
$168$	−4.60833	−0.355541
$169$	16.4166	1.26281
$170$	3.23901	0.248421
$171$	2.16645	0.165673
$172$	5.45957	0.416288
$173$	−8.63863	−0.656783	−0.328392	−	0.944542i	$-0.606507\pi$
$173$	−8.63863	−0.656783	−0.328392	+	0.944542i	$0.606507\pi$
$174$	2.04493	0.155026
$175$	9.29460	0.702605
$176$	0	0
$177$	3.38244	0.254240
$178$	−5.60537	−0.420141
$179$	−6.23923	−0.466342	−0.233171	−	0.972436i	$-0.574910\pi$
$179$	−6.23923	−0.466342	−0.233171	+	0.972436i	$0.574910\pi$
$180$	3.85031	0.286985
$181$	−26.1545	−1.94405	−0.972023	−	0.234884i	$-0.924529\pi$
$181$	−26.1545	−1.94405	−0.972023	+	0.234884i	$0.924529\pi$
$182$	−27.3763	−2.02927
$183$	2.64128	0.195249
$184$	5.61764	0.414138
$185$	17.9372	1.31877
$186$	0.352898	0.0258757
$187$	0	0
$188$	10.8132	0.788636
$189$	23.8087	1.73183
$190$	1.77724	0.128935
$191$	25.9985	1.88119	0.940594	−	0.339534i	$-0.110269\pi$
$191$	25.9985	1.88119	0.940594	+	0.339534i	$0.110269\pi$
$192$	0.912987	0.0658892
$193$	9.15782	0.659195	0.329597	−	0.944122i	$-0.393087\pi$
$193$	9.15782	0.659195	0.329597	+	0.944122i	$0.393087\pi$
$194$	−2.90528	−0.208587
$195$	−8.80050	−0.630217
$196$	18.4776	1.31983
$197$	−19.5680	−1.39416	−0.697080	−	0.716994i	$-0.745518\pi$
$197$	−19.5680	−1.39416	−0.697080	+	0.716994i	$0.745518\pi$
$198$	0	0
$199$	−14.8418	−1.05211	−0.526055	−	0.850451i	$-0.676329\pi$
$199$	−14.8418	−1.05211	−0.526055	+	0.850451i	$0.676329\pi$
$200$	−1.84141	−0.130208
$201$	−10.5591	−0.744784
$202$	−0.530731	−0.0373421
$203$	−11.3056	−0.793495
$204$	−1.66391	−0.116497
$205$	−16.4987	−1.15232
$206$	−3.63890	−0.253535
$207$	−12.1704	−0.845898
$208$	5.42371	0.376066
$209$	0	0
$210$	8.19012	0.565172
$211$	−17.6257	−1.21340	−0.606702	−	0.794930i	$-0.707508\pi$
$211$	−17.6257	−1.21340	−0.606702	+	0.794930i	$0.707508\pi$
$212$	6.85692	0.470935
$213$	−0.796820	−0.0545972
$214$	8.86825	0.606221
$215$	−9.70297	−0.661737
$216$	−4.71691	−0.320945
$217$	−1.95102	−0.132444
$218$	−2.02691	−0.137280
$219$	8.93099	0.603500
$220$	0	0
$221$	−9.88467	−0.664915
$222$	−9.21451	−0.618438
$223$	10.1395	0.678989	0.339495	−	0.940608i	$-0.389744\pi$
$223$	10.1395	0.678989	0.339495	+	0.940608i	$0.389744\pi$
$224$	−5.04753	−0.337252
$225$	3.98934	0.265956
$226$	1.61136	0.107186
$227$	9.16956	0.608605	0.304302	−	0.952575i	$-0.401577\pi$
$227$	9.16956	0.608605	0.304302	+	0.952575i	$0.401577\pi$
$228$	−0.912987	−0.0604641
$229$	−0.458204	−0.0302789	−0.0151395	−	0.999885i	$-0.504819\pi$
$229$	−0.458204	−0.0302789	−0.0151395	+	0.999885i	$0.504819\pi$
$230$	−9.98389	−0.658318
$231$	0	0
$232$	2.23982	0.147051
$233$	5.83823	0.382475	0.191237	−	0.981544i	$-0.438750\pi$
$233$	5.83823	0.382475	0.191237	+	0.981544i	$0.438750\pi$
$234$	−11.7502	−0.768135
$235$	−19.2177	−1.25363
$236$	3.70481	0.241163
$237$	8.50728	0.552607
$238$	9.19910	0.596289
$239$	7.69554	0.497783	0.248892	−	0.968531i	$-0.419934\pi$
$239$	7.69554	0.497783	0.248892	+	0.968531i	$0.419934\pi$
$240$	−1.62260	−0.104738
$241$	−11.2195	−0.722714	−0.361357	−	0.932428i	$-0.617686\pi$
$241$	−11.2195	−0.722714	−0.361357	+	0.932428i	$0.617686\pi$
$242$	0	0
$243$	16.1528	1.03620
$244$	2.89301	0.185206
$245$	−32.8391	−2.09801
$246$	8.47556	0.540382
$247$	−5.42371	−0.345102
$248$	0.386531	0.0245447
$249$	−3.91399	−0.248039
$250$	12.1588	0.768993
$251$	−2.94541	−0.185913	−0.0929563	−	0.995670i	$-0.529632\pi$
$251$	−2.94541	−0.185913	−0.0929563	+	0.995670i	$0.529632\pi$
$252$	10.9352	0.688856
$253$	0	0
$254$	15.7073	0.985566
$255$	2.95718	0.185186
$256$	1.00000	0.0625000
$257$	21.1881	1.32168	0.660839	−	0.750528i	$-0.270201\pi$
$257$	21.1881	1.32168	0.660839	+	0.750528i	$0.270201\pi$
$258$	4.98452	0.310322
$259$	50.9432	3.16546
$260$	−9.63923	−0.597800
$261$	−4.85247	−0.300360
$262$	13.6488	0.843226
$263$	3.78559	0.233430	0.116715	−	0.993165i	$-0.462764\pi$
$263$	3.78559	0.233430	0.116715	+	0.993165i	$0.462764\pi$
$264$	0	0
$265$	−12.1864	−0.748604
$266$	5.04753	0.309484
$267$	−5.11764	−0.313194
$268$	−11.5655	−0.706474
$269$	−29.0402	−1.77061	−0.885305	−	0.465010i	$-0.846051\pi$
$269$	−29.0402	−1.77061	−0.885305	+	0.465010i	$0.846051\pi$
$270$	8.38308	0.510178
$271$	16.5540	1.00559	0.502793	−	0.864407i	$-0.332306\pi$
$271$	16.5540	1.00559	0.502793	+	0.864407i	$0.332306\pi$
$272$	−1.82249	−0.110505
$273$	−24.9942	−1.51272
$274$	−9.02937	−0.545484
$275$	0	0
$276$	5.12883	0.308719
$277$	20.9258	1.25731	0.628656	−	0.777684i	$-0.283605\pi$
$277$	20.9258	1.25731	0.628656	+	0.777684i	$0.283605\pi$
$278$	10.3574	0.621194
$279$	−0.837401	−0.0501339
$280$	8.97068	0.536101
$281$	−8.63480	−0.515109	−0.257554	−	0.966264i	$-0.582917\pi$
$281$	−8.63480	−0.515109	−0.257554	+	0.966264i	$0.582917\pi$
$282$	9.87235	0.587890
$283$	6.31226	0.375225	0.187613	−	0.982243i	$-0.439925\pi$
$283$	6.31226	0.375225	0.187613	+	0.982243i	$0.439925\pi$
$284$	−0.872761	−0.0517888
$285$	1.62260	0.0961144
$286$	0	0
$287$	−46.8578	−2.76593
$288$	−2.16645	−0.127660
$289$	−13.6785	−0.804619
$290$	−3.98070	−0.233755
$291$	−2.65249	−0.155492
$292$	9.78216	0.572457
$293$	−12.6769	−0.740590	−0.370295	−	0.928914i	$-0.620743\pi$
$293$	−12.6769	−0.740590	−0.370295	+	0.928914i	$0.620743\pi$
$294$	16.8698	0.983866
$295$	−6.58434	−0.383355
$296$	−10.0927	−0.586627
$297$	0	0
$298$	14.2335	0.824523
$299$	30.4684	1.76203
$300$	−1.68119	−0.0970635
$301$	−27.5573	−1.58838
$302$	−14.2150	−0.817979
$303$	−0.484551	−0.0278367
$304$	−1.00000	−0.0573539
$305$	−5.14157	−0.294405
$306$	3.94835	0.225712
$307$	26.6423	1.52056	0.760279	−	0.649597i	$-0.225062\pi$
$307$	26.6423	1.52056	0.760279	+	0.649597i	$0.225062\pi$
$308$	0	0
$309$	−3.32227	−0.188998
$310$	−0.686958	−0.0390166
$311$	−25.0841	−1.42239	−0.711194	−	0.702995i	$-0.751845\pi$
$311$	−25.0841	−1.42239	−0.711194	+	0.702995i	$0.751845\pi$
$312$	4.95177	0.280339
$313$	34.1330	1.92931	0.964655	−	0.263518i	$-0.0848827\pi$
$313$	34.1330	1.92931	0.964655	+	0.263518i	$0.0848827\pi$
$314$	13.8523	0.781730
$315$	−19.4346	−1.09501
$316$	9.31807	0.524182
$317$	−30.1730	−1.69468	−0.847342	−	0.531048i	$-0.821798\pi$
$317$	−30.1730	−1.69468	−0.847342	+	0.531048i	$0.821798\pi$
$318$	6.26028	0.351059
$319$	0	0
$320$	−1.77724	−0.0993508
$321$	8.09660	0.451908
$322$	−28.3552	−1.58017
$323$	1.82249	0.101406
$324$	2.19288	0.121827
$325$	−9.98729	−0.553995
$326$	10.9348	0.605623
$327$	−1.85055	−0.102335
$328$	9.28332	0.512586
$329$	−54.5801	−3.00910
$330$	0	0
$331$	10.7721	0.592091	0.296045	−	0.955174i	$-0.404332\pi$
$331$	10.7721	0.592091	0.296045	+	0.955174i	$0.404332\pi$
$332$	−4.28702	−0.235281
$333$	21.8654	1.19822
$334$	3.90441	0.213640
$335$	20.5546	1.12302
$336$	−4.60833	−0.251405
$337$	−4.86374	−0.264945	−0.132472	−	0.991187i	$-0.542292\pi$
$337$	−4.86374	−0.264945	−0.132472	+	0.991187i	$0.542292\pi$
$338$	16.4166	0.892944
$339$	1.47115	0.0799019
$340$	3.23901	0.175660
$341$	0	0
$342$	2.16645	0.117148
$343$	−57.9333	−3.12811
$344$	5.45957	0.294360
$345$	−9.11517	−0.490744
$346$	−8.63863	−0.464416
$347$	8.80331	0.472586	0.236293	−	0.971682i	$-0.424067\pi$
$347$	8.80331	0.472586	0.236293	+	0.971682i	$0.424067\pi$
$348$	2.04493	0.109620
$349$	22.3320	1.19540	0.597702	−	0.801718i	$-0.296080\pi$
$349$	22.3320	1.19540	0.597702	+	0.801718i	$0.296080\pi$
$350$	9.29460	0.496817
$351$	−25.5831	−1.36553
$352$	0	0
$353$	−7.98769	−0.425142	−0.212571	−	0.977146i	$-0.568184\pi$
$353$	−7.98769	−0.425142	−0.212571	+	0.977146i	$0.568184\pi$
$354$	3.38244	0.179775
$355$	1.55111	0.0823242
$356$	−5.60537	−0.297084
$357$	8.39866	0.444504
$358$	−6.23923	−0.329754
$359$	−26.2639	−1.38615	−0.693077	−	0.720863i	$-0.743746\pi$
$359$	−26.2639	−1.38615	−0.693077	+	0.720863i	$0.743746\pi$
$360$	3.85031	0.202929
$361$	1.00000	0.0526316
$362$	−26.1545	−1.37465
$363$	0	0
$364$	−27.3763	−1.43491
$365$	−17.3852	−0.909985
$366$	2.64128	0.138062
$367$	−15.5072	−0.809468	−0.404734	−	0.914434i	$-0.632636\pi$
$367$	−15.5072	−0.809468	−0.404734	+	0.914434i	$0.632636\pi$
$368$	5.61764	0.292840
$369$	−20.1119	−1.04698
$370$	17.9372	0.932509
$371$	−34.6105	−1.79689
$372$	0.352898	0.0182969
$373$	−17.4626	−0.904179	−0.452090	−	0.891972i	$-0.649321\pi$
$373$	−17.4626	−0.904179	−0.452090	+	0.891972i	$0.649321\pi$
$374$	0	0
$375$	11.1009	0.573246
$376$	10.8132	0.557650
$377$	12.1481	0.625660
$378$	23.8087	1.22459
$379$	−31.6595	−1.62624	−0.813119	−	0.582097i	$-0.802232\pi$
$379$	−31.6595	−1.62624	−0.813119	+	0.582097i	$0.802232\pi$
$380$	1.77724	0.0911705
$381$	14.3406	0.734692
$382$	25.9985	1.33020
$383$	−6.09885	−0.311637	−0.155818	−	0.987786i	$-0.549801\pi$
$383$	−6.09885	−0.311637	−0.155818	+	0.987786i	$0.549801\pi$
$384$	0.912987	0.0465907
$385$	0	0
$386$	9.15782	0.466121
$387$	−11.8279	−0.601246
$388$	−2.90528	−0.147493
$389$	−32.0224	−1.62360	−0.811801	−	0.583934i	$-0.801513\pi$
$389$	−32.0224	−1.62360	−0.811801	+	0.583934i	$0.801513\pi$
$390$	−8.80050	−0.445630
$391$	−10.2381	−0.517764
$392$	18.4776	0.933258
$393$	12.4612	0.628583
$394$	−19.5680	−0.985819
$395$	−16.5605	−0.833247
$396$	0	0
$397$	10.0101	0.502395	0.251197	−	0.967936i	$-0.419176\pi$
$397$	10.0101	0.502395	0.251197	+	0.967936i	$0.419176\pi$
$398$	−14.8418	−0.743954
$399$	4.60833	0.230705
$400$	−1.84141	−0.0920707
$401$	−5.31105	−0.265221	−0.132611	−	0.991168i	$-0.542336\pi$
$401$	−5.31105	−0.265221	−0.132611	+	0.991168i	$0.542336\pi$
$402$	−10.5591	−0.526642
$403$	2.09643	0.104431
$404$	−0.530731	−0.0264049
$405$	−3.89728	−0.193658
$406$	−11.3056	−0.561085
$407$	0	0
$408$	−1.66391	−0.0823760
$409$	18.5420	0.916843	0.458421	−	0.888735i	$-0.348415\pi$
$409$	18.5420	0.916843	0.458421	+	0.888735i	$0.348415\pi$
$410$	−16.4987	−0.814813
$411$	−8.24371	−0.406632
$412$	−3.63890	−0.179276
$413$	−18.7001	−0.920174
$414$	−12.1704	−0.598140
$415$	7.61906	0.374005
$416$	5.42371	0.265919
$417$	9.45615	0.463069
$418$	0	0
$419$	11.5438	0.563953	0.281977	−	0.959421i	$-0.409010\pi$
$419$	11.5438	0.563953	0.281977	+	0.959421i	$0.409010\pi$
$420$	8.19012	0.399637
$421$	33.7279	1.64380	0.821899	−	0.569633i	$-0.192914\pi$
$421$	33.7279	1.64380	0.821899	+	0.569633i	$0.192914\pi$
$422$	−17.6257	−0.858006
$423$	−23.4264	−1.13903
$424$	6.85692	0.333001
$425$	3.35597	0.162788
$426$	−0.796820	−0.0386060
$427$	−14.6025	−0.706666
$428$	8.86825	0.428663
$429$	0	0
$430$	−9.70297	−0.467919
$431$	−10.0313	−0.483189	−0.241595	−	0.970377i	$-0.577670\pi$
$431$	−10.0313	−0.483189	−0.241595	+	0.970377i	$0.577670\pi$
$432$	−4.71691	−0.226942
$433$	−7.90731	−0.380001	−0.190001	−	0.981784i	$-0.560849\pi$
$433$	−7.90731	−0.380001	−0.190001	+	0.981784i	$0.560849\pi$
$434$	−1.95102	−0.0936522
$435$	−3.63433	−0.174253
$436$	−2.02691	−0.0970716
$437$	−5.61764	−0.268728
$438$	8.93099	0.426739
$439$	25.7405	1.22853	0.614263	−	0.789102i	$-0.289453\pi$
$439$	25.7405	1.22853	0.614263	+	0.789102i	$0.289453\pi$
$440$	0	0
$441$	−40.0308	−1.90623
$442$	−9.88467	−0.470166
$443$	−24.2023	−1.14988	−0.574942	−	0.818194i	$-0.694975\pi$
$443$	−24.2023	−1.14988	−0.574942	+	0.818194i	$0.694975\pi$
$444$	−9.21451	−0.437301
$445$	9.96210	0.472249
$446$	10.1395	0.480118
$447$	12.9950	0.614641
$448$	−5.04753	−0.238473
$449$	36.5068	1.72286	0.861430	−	0.507876i	$-0.169569\pi$
$449$	36.5068	1.72286	0.861430	+	0.507876i	$0.169569\pi$
$450$	3.98934	0.188059
$451$	0	0
$452$	1.61136	0.0757919
$453$	−12.9781	−0.609763
$454$	9.16956	0.430349
$455$	48.6543	2.28095
$456$	−0.912987	−0.0427546
$457$	15.7612	0.737277	0.368639	−	0.929573i	$-0.379824\pi$
$457$	15.7612	0.737277	0.368639	+	0.929573i	$0.379824\pi$
$458$	−0.458204	−0.0214105
$459$	8.59654	0.401252
$460$	−9.98389	−0.465501
$461$	6.61141	0.307924	0.153962	−	0.988077i	$-0.450797\pi$
$461$	6.61141	0.307924	0.153962	+	0.988077i	$0.450797\pi$
$462$	0	0
$463$	−32.4747	−1.50923	−0.754614	−	0.656169i	$-0.772176\pi$
$463$	−32.4747	−1.50923	−0.754614	+	0.656169i	$0.772176\pi$
$464$	2.23982	0.103981
$465$	−0.627184	−0.0290850
$466$	5.83823	0.270451
$467$	38.0595	1.76118	0.880592	−	0.473876i	$-0.157146\pi$
$467$	38.0595	1.76118	0.880592	+	0.473876i	$0.157146\pi$
$468$	−11.7502	−0.543154
$469$	58.3771	2.69560
$470$	−19.2177	−0.886448
$471$	12.6470	0.582742
$472$	3.70481	0.170528
$473$	0	0
$474$	8.50728	0.390752
$475$	1.84141	0.0844899
$476$	9.19910	0.421640
$477$	−14.8552	−0.680173
$478$	7.69554	0.351986
$479$	30.0892	1.37481	0.687405	−	0.726274i	$-0.258750\pi$
$479$	30.0892	1.37481	0.687405	+	0.726274i	$0.258750\pi$
$480$	−1.62260	−0.0740612
$481$	−54.7399	−2.49592
$482$	−11.2195	−0.511036
$483$	−25.8879	−1.17794
$484$	0	0
$485$	5.16339	0.234457
$486$	16.1528	0.732706
$487$	−2.69394	−0.122074	−0.0610370	−	0.998136i	$-0.519441\pi$
$487$	−2.69394	−0.122074	−0.0610370	+	0.998136i	$0.519441\pi$
$488$	2.89301	0.130960
$489$	9.98334	0.451462
$490$	−32.8391	−1.48352
$491$	27.8830	1.25834	0.629171	−	0.777267i	$-0.283394\pi$
$491$	27.8830	1.25834	0.629171	+	0.777267i	$0.283394\pi$
$492$	8.47556	0.382108
$493$	−4.08206	−0.183847
$494$	−5.42371	−0.244024
$495$	0	0
$496$	0.386531	0.0173557
$497$	4.40529	0.197604
$498$	−3.91399	−0.175390
$499$	21.0031	0.940229	0.470115	−	0.882605i	$-0.344213\pi$
$499$	21.0031	0.940229	0.470115	+	0.882605i	$0.344213\pi$
$500$	12.1588	0.543760
$501$	3.56467	0.159258
$502$	−2.94541	−0.131460
$503$	−10.6716	−0.475822	−0.237911	−	0.971287i	$-0.576463\pi$
$503$	−10.6716	−0.475822	−0.237911	+	0.971287i	$0.576463\pi$
$504$	10.9352	0.487094
$505$	0.943237	0.0419735
$506$	0	0
$507$	14.9881	0.665646
$508$	15.7073	0.696901
$509$	−13.7570	−0.609767	−0.304884	−	0.952390i	$-0.598618\pi$
$509$	−13.7570	−0.609767	−0.304884	+	0.952390i	$0.598618\pi$
$510$	2.95718	0.130946
$511$	−49.3757	−2.18425
$512$	1.00000	0.0441942
$513$	4.71691	0.208257
$514$	21.1881	0.934567
$515$	6.46721	0.284979
$516$	4.98452	0.219431
$517$	0	0
$518$	50.9432	2.23832
$519$	−7.88696	−0.346199
$520$	−9.63923	−0.422708
$521$	−5.73245	−0.251143	−0.125572	−	0.992085i	$-0.540076\pi$
$521$	−5.73245	−0.251143	−0.125572	+	0.992085i	$0.540076\pi$
$522$	−4.85247	−0.212387
$523$	13.7126	0.599612	0.299806	−	0.954000i	$-0.403078\pi$
$523$	13.7126	0.599612	0.299806	+	0.954000i	$0.403078\pi$
$524$	13.6488	0.596250
$525$	8.48585	0.370353
$526$	3.78559	0.165060
$527$	−0.704450	−0.0306863
$528$	0	0
$529$	8.55784	0.372080
$530$	−12.1864	−0.529343
$531$	−8.02630	−0.348312
$532$	5.04753	0.218838
$533$	50.3500	2.18090
$534$	−5.11764	−0.221462
$535$	−15.7610	−0.681408
$536$	−11.5655	−0.499552
$537$	−5.69634	−0.245815
$538$	−29.0402	−1.25201
$539$	0	0
$540$	8.38308	0.360750
$541$	−9.98640	−0.429349	−0.214674	−	0.976686i	$-0.568869\pi$
$541$	−9.98640	−0.429349	−0.214674	+	0.976686i	$0.568869\pi$
$542$	16.5540	0.711057
$543$	−23.8787	−1.02473
$544$	−1.82249	−0.0781388
$545$	3.60231	0.154306
$546$	−24.9942	−1.06965
$547$	−1.14622	−0.0490088	−0.0245044	−	0.999700i	$-0.507801\pi$
$547$	−1.14622	−0.0490088	−0.0245044	+	0.999700i	$0.507801\pi$
$548$	−9.02937	−0.385716
$549$	−6.26757	−0.267493
$550$	0	0
$551$	−2.23982	−0.0954195
$552$	5.12883	0.218298
$553$	−47.0332	−2.00006
$554$	20.9258	0.889054
$555$	16.3764	0.695140
$556$	10.3574	0.439250
$557$	−29.4129	−1.24626	−0.623132	−	0.782117i	$-0.714140\pi$
$557$	−29.4129	−1.24626	−0.623132	+	0.782117i	$0.714140\pi$
$558$	−0.837401	−0.0354500
$559$	29.6111	1.25242
$560$	8.97068	0.379080
$561$	0	0
$562$	−8.63480	−0.364237
$563$	3.52757	0.148669	0.0743347	−	0.997233i	$-0.476317\pi$
$563$	3.52757	0.148669	0.0743347	+	0.997233i	$0.476317\pi$
$564$	9.87235	0.415701
$565$	−2.86377	−0.120480
$566$	6.31226	0.265324
$567$	−11.0687	−0.464840
$568$	−0.872761	−0.0366202
$569$	23.4396	0.982638	0.491319	−	0.870980i	$-0.336515\pi$
$569$	23.4396	0.982638	0.491319	+	0.870980i	$0.336515\pi$
$570$	1.62260	0.0679632
$571$	23.7470	0.993782	0.496891	−	0.867813i	$-0.334475\pi$
$571$	23.7470	0.993782	0.496891	+	0.867813i	$0.334475\pi$
$572$	0	0
$573$	23.7363	0.991599
$574$	−46.8578	−1.95581
$575$	−10.3444	−0.431391
$576$	−2.16645	−0.0902689
$577$	−12.3050	−0.512263	−0.256131	−	0.966642i	$-0.582448\pi$
$577$	−12.3050	−0.512263	−0.256131	+	0.966642i	$0.582448\pi$
$578$	−13.6785	−0.568951
$579$	8.36098	0.347470
$580$	−3.98070	−0.165290
$581$	21.6389	0.897731
$582$	−2.65249	−0.109949
$583$	0	0
$584$	9.78216	0.404789
$585$	20.8830	0.863404
$586$	−12.6769	−0.523676
$587$	−25.7463	−1.06266	−0.531332	−	0.847164i	$-0.678308\pi$
$587$	−25.7463	−1.06266	−0.531332	+	0.847164i	$0.678308\pi$
$588$	16.8698	0.695698
$589$	−0.386531	−0.0159267
$590$	−6.58434	−0.271073
$591$	−17.8653	−0.734880
$592$	−10.0927	−0.414808
$593$	13.4292	0.551469	0.275735	−	0.961234i	$-0.411079\pi$
$593$	13.4292	0.551469	0.275735	+	0.961234i	$0.411079\pi$
$594$	0	0
$595$	−16.3490	−0.670244
$596$	14.2335	0.583026
$597$	−13.5504	−0.554581
$598$	30.4684	1.24595
$599$	33.1006	1.35245	0.676227	−	0.736693i	$-0.263614\pi$
$599$	33.1006	1.35245	0.676227	+	0.736693i	$0.263614\pi$
$600$	−1.68119	−0.0686342
$601$	−34.6197	−1.41217	−0.706084	−	0.708128i	$-0.749540\pi$
$601$	−34.6197	−1.41217	−0.706084	+	0.708128i	$0.749540\pi$
$602$	−27.5573	−1.12315
$603$	25.0561	1.02036
$604$	−14.2150	−0.578398
$605$	0	0
$606$	−0.484551	−0.0196835
$607$	−39.6229	−1.60824	−0.804122	−	0.594465i	$-0.797364\pi$
$607$	−39.6229	−1.60824	−0.804122	+	0.594465i	$0.797364\pi$
$608$	−1.00000	−0.0405554
$609$	−10.3218	−0.418262
$610$	−5.14157	−0.208176
$611$	58.6478	2.37264
$612$	3.94835	0.159603
$613$	21.7299	0.877661	0.438831	−	0.898570i	$-0.355393\pi$
$613$	21.7299	0.877661	0.438831	+	0.898570i	$0.355393\pi$
$614$	26.6423	1.07520
$615$	−15.0631	−0.607403
$616$	0	0
$617$	7.82581	0.315055	0.157528	−	0.987515i	$-0.449648\pi$
$617$	7.82581	0.315055	0.157528	+	0.987515i	$0.449648\pi$
$618$	−3.32227	−0.133641
$619$	−13.4660	−0.541242	−0.270621	−	0.962686i	$-0.587229\pi$
$619$	−13.4660	−0.541242	−0.270621	+	0.962686i	$0.587229\pi$
$620$	−0.686958	−0.0275889
$621$	−26.4979	−1.06332
$622$	−25.0841	−1.00578
$623$	28.2933	1.13355
$624$	4.95177	0.198230
$625$	−12.4021	−0.496085
$626$	34.1330	1.36423
$627$	0	0
$628$	13.8523	0.552767
$629$	18.3939	0.733413
$630$	−19.4346	−0.774291
$631$	17.7750	0.707611	0.353806	−	0.935319i	$-0.384887\pi$
$631$	17.7750	0.707611	0.353806	+	0.935319i	$0.384887\pi$
$632$	9.31807	0.370653
$633$	−16.0920	−0.639601
$634$	−30.1730	−1.19832
$635$	−27.9157	−1.10780
$636$	6.26028	0.248236
$637$	100.217	3.97074
$638$	0	0
$639$	1.89080	0.0747988
$640$	−1.77724	−0.0702516
$641$	29.8405	1.17863	0.589315	−	0.807903i	$-0.299398\pi$
$641$	29.8405	1.17863	0.589315	+	0.807903i	$0.299398\pi$
$642$	8.09660	0.319547
$643$	−19.4161	−0.765698	−0.382849	−	0.923811i	$-0.625057\pi$
$643$	−19.4161	−0.765698	−0.382849	+	0.923811i	$0.625057\pi$
$644$	−28.3552	−1.11735
$645$	−8.85869	−0.348810
$646$	1.82249	0.0717051
$647$	−22.9533	−0.902388	−0.451194	−	0.892426i	$-0.649002\pi$
$647$	−22.9533	−0.902388	−0.451194	+	0.892426i	$0.649002\pi$
$648$	2.19288	0.0861446
$649$	0	0
$650$	−9.98729	−0.391734
$651$	−1.78126	−0.0698131
$652$	10.9348	0.428240
$653$	35.1675	1.37621	0.688105	−	0.725611i	$-0.258443\pi$
$653$	35.1675	1.37621	0.688105	+	0.725611i	$0.258443\pi$
$654$	−1.85055	−0.0723621
$655$	−24.2572	−0.947807
$656$	9.28332	0.362453
$657$	−21.1926	−0.826802
$658$	−54.5801	−2.12776
$659$	14.4098	0.561325	0.280662	−	0.959807i	$-0.409446\pi$
$659$	14.4098	0.561325	0.280662	+	0.959807i	$0.409446\pi$
$660$	0	0
$661$	−19.8395	−0.771668	−0.385834	−	0.922568i	$-0.626086\pi$
$661$	−19.8395	−0.771668	−0.385834	+	0.922568i	$0.626086\pi$
$662$	10.7721	0.418671
$663$	−9.02458	−0.350486
$664$	−4.28702	−0.166369
$665$	−8.97068	−0.347868
$666$	21.8654	0.847266
$667$	12.5825	0.487196
$668$	3.90441	0.151066
$669$	9.25721	0.357905
$670$	20.5546	0.794095
$671$	0	0
$672$	−4.60833	−0.177770
$673$	17.3731	0.669685	0.334843	−	0.942274i	$-0.391317\pi$
$673$	17.3731	0.669685	0.334843	+	0.942274i	$0.391317\pi$
$674$	−4.86374	−0.187344
$675$	8.68578	0.334316
$676$	16.4166	0.631407
$677$	−12.7384	−0.489577	−0.244789	−	0.969576i	$-0.578719\pi$
$677$	−12.7384	−0.489577	−0.244789	+	0.969576i	$0.578719\pi$
$678$	1.47115	0.0564992
$679$	14.6645	0.562772
$680$	3.23901	0.124210
$681$	8.37169	0.320804
$682$	0	0
$683$	3.11068	0.119027	0.0595134	−	0.998228i	$-0.481045\pi$
$683$	3.11068	0.119027	0.0595134	+	0.998228i	$0.481045\pi$
$684$	2.16645	0.0828364
$685$	16.0474	0.613139
$686$	−57.9333	−2.21191
$687$	−0.418334	−0.0159604
$688$	5.45957	0.208144
$689$	37.1899	1.41682
$690$	−9.11517	−0.347009
$691$	34.6675	1.31881	0.659407	−	0.751786i	$-0.270807\pi$
$691$	34.6675	1.31881	0.659407	+	0.751786i	$0.270807\pi$
$692$	−8.63863	−0.328392
$693$	0	0
$694$	8.80331	0.334169
$695$	−18.4075	−0.698238
$696$	2.04493	0.0775128
$697$	−16.9188	−0.640845
$698$	22.3320	0.845279
$699$	5.33023	0.201608
$700$	9.29460	0.351303
$701$	−1.33992	−0.0506079	−0.0253040	−	0.999680i	$-0.508055\pi$
$701$	−1.33992	−0.0506079	−0.0253040	+	0.999680i	$0.508055\pi$
$702$	−25.5831	−0.965573
$703$	10.0927	0.380654
$704$	0	0
$705$	−17.5455	−0.660803
$706$	−7.98769	−0.300621
$707$	2.67888	0.100750
$708$	3.38244	0.127120
$709$	−14.2636	−0.535681	−0.267841	−	0.963463i	$-0.586310\pi$
$709$	−14.2636	−0.535681	−0.267841	+	0.963463i	$0.586310\pi$
$710$	1.55111	0.0582120
$711$	−20.1872	−0.757078
$712$	−5.60537	−0.210070
$713$	2.17139	0.0813191
$714$	8.39866	0.314312
$715$	0	0
$716$	−6.23923	−0.233171
$717$	7.02593	0.262388
$718$	−26.2639	−0.980160
$719$	−32.6745	−1.21855	−0.609276	−	0.792958i	$-0.708540\pi$
$719$	−32.6745	−1.21855	−0.609276	+	0.792958i	$0.708540\pi$
$720$	3.85031	0.143493
$721$	18.3675	0.684041
$722$	1.00000	0.0372161
$723$	−10.2433	−0.380952
$724$	−26.1545	−0.972023
$725$	−4.12444	−0.153178
$726$	0	0
$727$	−7.95801	−0.295146	−0.147573	−	0.989051i	$-0.547146\pi$
$727$	−7.95801	−0.295146	−0.147573	+	0.989051i	$0.547146\pi$
$728$	−27.3763	−1.01463
$729$	8.16865	0.302543
$730$	−17.3852	−0.643457
$731$	−9.95003	−0.368015
$732$	2.64128	0.0976245
$733$	−23.8742	−0.881812	−0.440906	−	0.897553i	$-0.645343\pi$
$733$	−23.8742	−0.881812	−0.440906	+	0.897553i	$0.645343\pi$
$734$	−15.5072	−0.572380
$735$	−29.9817	−1.10589
$736$	5.61764	0.207069
$737$	0	0
$738$	−20.1119	−0.740329
$739$	−8.25266	−0.303579	−0.151790	−	0.988413i	$-0.548504\pi$
$739$	−8.25266	−0.303579	−0.151790	+	0.988413i	$0.548504\pi$
$740$	17.9372	0.659383
$741$	−4.95177	−0.181908
$742$	−34.6105	−1.27059
$743$	−4.22346	−0.154944	−0.0774718	−	0.996995i	$-0.524685\pi$
$743$	−4.22346	−0.154944	−0.0774718	+	0.996995i	$0.524685\pi$
$744$	0.352898	0.0129379
$745$	−25.2963	−0.926785
$746$	−17.4626	−0.639351
$747$	9.28763	0.339817
$748$	0	0
$749$	−44.7628	−1.63560
$750$	11.1009	0.405346
$751$	35.6180	1.29972	0.649859	−	0.760055i	$-0.274828\pi$
$751$	35.6180	1.29972	0.649859	+	0.760055i	$0.274828\pi$
$752$	10.8132	0.394318
$753$	−2.68912	−0.0979970
$754$	12.1481	0.442408
$755$	25.2634	0.919429
$756$	23.8087	0.865915
$757$	38.4502	1.39749	0.698747	−	0.715369i	$-0.253741\pi$
$757$	38.4502	1.39749	0.698747	+	0.715369i	$0.253741\pi$
$758$	−31.6595	−1.14992
$759$	0	0
$760$	1.77724	0.0644673
$761$	2.50805	0.0909168	0.0454584	−	0.998966i	$-0.485525\pi$
$761$	2.50805	0.0909168	0.0454584	+	0.998966i	$0.485525\pi$
$762$	14.3406	0.519505
$763$	10.2309	0.370384
$764$	25.9985	0.940594
$765$	−7.01717	−0.253706
$766$	−6.09885	−0.220360
$767$	20.0938	0.725545
$768$	0.912987	0.0329446
$769$	1.24222	0.0447955	0.0223978	−	0.999749i	$-0.492870\pi$
$769$	1.24222	0.0447955	0.0223978	+	0.999749i	$0.492870\pi$
$770$	0	0
$771$	19.3445	0.696674
$772$	9.15782	0.329597
$773$	26.8350	0.965189	0.482595	−	0.875844i	$-0.339694\pi$
$773$	26.8350	0.965189	0.482595	+	0.875844i	$0.339694\pi$
$774$	−11.8279	−0.425145
$775$	−0.711763	−0.0255673
$776$	−2.90528	−0.104294
$777$	46.5105	1.66856
$778$	−32.0224	−1.14806
$779$	−9.28332	−0.332609
$780$	−8.80050	−0.315108
$781$	0	0
$782$	−10.2381	−0.366114
$783$	−10.5650	−0.377563
$784$	18.4776	0.659913
$785$	−24.6189	−0.878685
$786$	12.4612	0.444476
$787$	4.79827	0.171040	0.0855200	−	0.996336i	$-0.472745\pi$
$787$	4.79827	0.171040	0.0855200	+	0.996336i	$0.472745\pi$
$788$	−19.5680	−0.697080
$789$	3.45620	0.123044
$790$	−16.5605	−0.589195
$791$	−8.13338	−0.289190
$792$	0	0
$793$	15.6908	0.557197
$794$	10.0101	0.355247
$795$	−11.1260	−0.394600
$796$	−14.8418	−0.526055
$797$	−4.15409	−0.147146	−0.0735728	−	0.997290i	$-0.523440\pi$
$797$	−4.15409	−0.147146	−0.0735728	+	0.997290i	$0.523440\pi$
$798$	4.60833	0.163133
$799$	−19.7071	−0.697186
$800$	−1.84141	−0.0651038
$801$	12.1438	0.429080
$802$	−5.31105	−0.187540
$803$	0	0
$804$	−10.5591	−0.372392
$805$	50.3940	1.77616
$806$	2.09643	0.0738435
$807$	−26.5133	−0.933313
$808$	−0.530731	−0.0186711
$809$	−17.9486	−0.631039	−0.315520	−	0.948919i	$-0.602179\pi$
$809$	−17.9486	−0.631039	−0.315520	+	0.948919i	$0.602179\pi$
$810$	−3.89728	−0.136937
$811$	−8.31396	−0.291943	−0.145971	−	0.989289i	$-0.546631\pi$
$811$	−8.31396	−0.291943	−0.145971	+	0.989289i	$0.546631\pi$
$812$	−11.3056	−0.396747
$813$	15.1136	0.530058
$814$	0	0
$815$	−19.4338	−0.680736
$816$	−1.66391	−0.0582487
$817$	−5.45957	−0.191006
$818$	18.5420	0.648306
$819$	59.3095	2.07244
$820$	−16.4987	−0.576160
$821$	50.0923	1.74823	0.874116	−	0.485716i	$-0.161441\pi$
$821$	50.0923	1.74823	0.874116	+	0.485716i	$0.161441\pi$
$822$	−8.24371	−0.287532
$823$	26.9086	0.937974	0.468987	−	0.883205i	$-0.344619\pi$
$823$	26.9086	0.937974	0.468987	+	0.883205i	$0.344619\pi$
$824$	−3.63890	−0.126767
$825$	0	0
$826$	−18.7001	−0.650661
$827$	6.87811	0.239175	0.119588	−	0.992824i	$-0.461843\pi$
$827$	6.87811	0.239175	0.119588	+	0.992824i	$0.461843\pi$
$828$	−12.1704	−0.422949
$829$	26.0817	0.905856	0.452928	−	0.891547i	$-0.350379\pi$
$829$	26.0817	0.905856	0.452928	+	0.891547i	$0.350379\pi$
$830$	7.61906	0.264462
$831$	19.1050	0.662746
$832$	5.42371	0.188033
$833$	−33.6753	−1.16678
$834$	9.45615	0.327440
$835$	−6.93907	−0.240136
$836$	0	0
$837$	−1.82323	−0.0630200
$838$	11.5438	0.398775
$839$	29.8292	1.02982	0.514910	−	0.857244i	$-0.327825\pi$
$839$	29.8292	1.02982	0.514910	+	0.857244i	$0.327825\pi$
$840$	8.19012	0.282586
$841$	−23.9832	−0.827007
$842$	33.7279	1.16234
$843$	−7.88346	−0.271521
$844$	−17.6257	−0.606702
$845$	−29.1762	−1.00369
$846$	−23.4264	−0.805416
$847$	0	0
$848$	6.85692	0.235468
$849$	5.76302	0.197786
$850$	3.35597	0.115109
$851$	−56.6972	−1.94355
$852$	−0.796820	−0.0272986
$853$	−35.7549	−1.22423	−0.612113	−	0.790770i	$-0.709680\pi$
$853$	−35.7549	−1.22423	−0.612113	+	0.790770i	$0.709680\pi$
$854$	−14.6025	−0.499689
$855$	−3.85031	−0.131678
$856$	8.86825	0.303111
$857$	−53.7988	−1.83773	−0.918867	−	0.394568i	$-0.870894\pi$
$857$	−53.7988	−1.83773	−0.918867	+	0.394568i	$0.870894\pi$
$858$	0	0
$859$	40.7851	1.39157	0.695785	−	0.718250i	$-0.255057\pi$
$859$	40.7851	1.39157	0.695785	+	0.718250i	$0.255057\pi$
$860$	−9.70297	−0.330868
$861$	−42.7806	−1.45796
$862$	−10.0313	−0.341666
$863$	−34.9318	−1.18909	−0.594546	−	0.804062i	$-0.702668\pi$
$863$	−34.9318	−1.18909	−0.594546	+	0.804062i	$0.702668\pi$
$864$	−4.71691	−0.160472
$865$	15.3529	0.522015
$866$	−7.90731	−0.268701
$867$	−12.4883	−0.424125
$868$	−1.95102	−0.0662221
$869$	0	0
$870$	−3.63433	−0.123215
$871$	−62.7277	−2.12545
$872$	−2.02691	−0.0686400
$873$	6.29416	0.213025
$874$	−5.61764	−0.190019
$875$	−61.3721	−2.07476
$876$	8.93099	0.301750
$877$	−2.35793	−0.0796218	−0.0398109	−	0.999207i	$-0.512676\pi$
$877$	−2.35793	−0.0796218	−0.0398109	+	0.999207i	$0.512676\pi$
$878$	25.7405	0.868699
$879$	−11.5738	−0.390375
$880$	0	0
$881$	24.8750	0.838060	0.419030	−	0.907972i	$-0.362370\pi$
$881$	24.8750	0.838060	0.419030	+	0.907972i	$0.362370\pi$
$882$	−40.0308	−1.34791
$883$	35.8838	1.20759	0.603793	−	0.797141i	$-0.293655\pi$
$883$	35.8838	1.20759	0.603793	+	0.797141i	$0.293655\pi$
$884$	−9.88467	−0.332457
$885$	−6.01142	−0.202072
$886$	−24.2023	−0.813091
$887$	−49.9066	−1.67570	−0.837850	−	0.545901i	$-0.816188\pi$
$887$	−49.9066	−1.67570	−0.837850	+	0.545901i	$0.816188\pi$
$888$	−9.21451	−0.309219
$889$	−79.2833	−2.65908
$890$	9.96210	0.333930
$891$	0	0
$892$	10.1395	0.339495
$893$	−10.8132	−0.361851
$894$	12.9950	0.434617
$895$	11.0886	0.370652
$896$	−5.04753	−0.168626
$897$	27.8173	0.928792
$898$	36.5068	1.21825
$899$	0.865759	0.0288747
$900$	3.98934	0.132978
$901$	−12.4967	−0.416325
$902$	0	0
$903$	−25.1595	−0.837256
$904$	1.61136	0.0535930
$905$	46.4828	1.54514
$906$	−12.9781	−0.431168
$907$	−4.36413	−0.144909	−0.0724543	−	0.997372i	$-0.523083\pi$
$907$	−4.36413	−0.144909	−0.0724543	+	0.997372i	$0.523083\pi$
$908$	9.16956	0.304302
$909$	1.14980	0.0381366
$910$	48.6543	1.61287
$911$	45.2710	1.49989	0.749947	−	0.661498i	$-0.230079\pi$
$911$	45.2710	1.49989	0.749947	+	0.661498i	$0.230079\pi$
$912$	−0.912987	−0.0302320
$913$	0	0
$914$	15.7612	0.521334
$915$	−4.69419	−0.155185
$916$	−0.458204	−0.0151395
$917$	−68.8927	−2.27504
$918$	8.59654	0.283728
$919$	−50.6574	−1.67103	−0.835517	−	0.549464i	$-0.814832\pi$
$919$	−50.6574	−1.67103	−0.835517	+	0.549464i	$0.814832\pi$
$920$	−9.98389	−0.329159
$921$	24.3241	0.801507
$922$	6.61141	0.217735
$923$	−4.73360	−0.155808
$924$	0	0
$925$	18.5849	0.611066
$926$	−32.4747	−1.06719
$927$	7.88352	0.258929
$928$	2.23982	0.0735257
$929$	−1.41717	−0.0464958	−0.0232479	−	0.999730i	$-0.507401\pi$
$929$	−1.41717	−0.0464958	−0.0232479	+	0.999730i	$0.507401\pi$
$930$	−0.627184	−0.0205662
$931$	−18.4776	−0.605578
$932$	5.83823	0.191237
$933$	−22.9015	−0.749760
$934$	38.0595	1.24534
$935$	0	0
$936$	−11.7502	−0.384068
$937$	0.392294	0.0128157	0.00640784	−	0.999979i	$-0.497960\pi$
$937$	0.392294	0.0128157	0.00640784	+	0.999979i	$0.497960\pi$
$938$	58.3771	1.90608
$939$	31.1630	1.01696
$940$	−19.2177	−0.626813
$941$	24.7594	0.807132	0.403566	−	0.914950i	$-0.367771\pi$
$941$	24.7594	0.807132	0.403566	+	0.914950i	$0.367771\pi$
$942$	12.6470	0.412060
$943$	52.1503	1.69825
$944$	3.70481	0.120581
$945$	−42.3139	−1.37647
$946$	0	0
$947$	30.8771	1.00337	0.501685	−	0.865050i	$-0.332714\pi$
$947$	30.8771	1.00337	0.501685	+	0.865050i	$0.332714\pi$
$948$	8.50728	0.276304
$949$	53.0555	1.72226
$950$	1.84141	0.0597434
$951$	−27.5475	−0.893290
$952$	9.19910	0.298144
$953$	7.78750	0.252262	0.126131	−	0.992014i	$-0.459744\pi$
$953$	7.78750	0.252262	0.126131	+	0.992014i	$0.459744\pi$
$954$	−14.8552	−0.480955
$955$	−46.2057	−1.49518
$956$	7.69554	0.248892
$957$	0	0
$958$	30.0892	0.972138
$959$	45.5760	1.47173
$960$	−1.62260	−0.0523691
$961$	−30.8506	−0.995180
$962$	−54.7399	−1.76488
$963$	−19.2127	−0.619119
$964$	−11.2195	−0.361357
$965$	−16.2757	−0.523932
$966$	−25.8879	−0.832931
$967$	13.5476	0.435662	0.217831	−	0.975987i	$-0.430102\pi$
$967$	13.5476	0.435662	0.217831	+	0.975987i	$0.430102\pi$
$968$	0	0
$969$	1.66391	0.0534526
$970$	5.16339	0.165786
$971$	45.5661	1.46229	0.731143	−	0.682224i	$-0.238987\pi$
$971$	45.5661	1.46229	0.731143	+	0.682224i	$0.238987\pi$
$972$	16.1528	0.518101
$973$	−52.2791	−1.67599
$974$	−2.69394	−0.0863193
$975$	−9.11827	−0.292018
$976$	2.89301	0.0926029
$977$	−21.4985	−0.687796	−0.343898	−	0.939007i	$-0.611748\pi$
$977$	−21.4985	−0.687796	−0.343898	+	0.939007i	$0.611748\pi$
$978$	9.98334	0.319232
$979$	0	0
$980$	−32.8391	−1.04901
$981$	4.39122	0.140201
$982$	27.8830	0.889783
$983$	13.6341	0.434862	0.217431	−	0.976076i	$-0.430232\pi$
$983$	13.6341	0.434862	0.217431	+	0.976076i	$0.430232\pi$
$984$	8.47556	0.270191
$985$	34.7770	1.10809
$986$	−4.08206	−0.129999
$987$	−49.8310	−1.58614
$988$	−5.42371	−0.172551
$989$	30.6699	0.975245
$990$	0	0
$991$	16.9742	0.539202	0.269601	−	0.962972i	$-0.413108\pi$
$991$	16.9742	0.539202	0.269601	+	0.962972i	$0.413108\pi$
$992$	0.386531	0.0122724
$993$	9.83483	0.312099
$994$	4.40529	0.139727
$995$	26.3775	0.836223
$996$	−3.91399	−0.124020
$997$	−40.8048	−1.29230	−0.646150	−	0.763211i	$-0.723622\pi$
$997$	−40.8048	−1.29230	−0.646150	+	0.763211i	$0.723622\pi$
$998$	21.0031	0.664843
$999$	47.6064	1.50620

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4598.2.a.ca.1.5		8
11.3	even	5		418.2.f.f.229.2	yes	16
11.4	even	5		418.2.f.f.115.2	✓	16
11.10	odd	2		4598.2.a.bx.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.f.f.115.2	✓	16	11.4	even	5
418.2.f.f.229.2	yes	16	11.3	even	5
4598.2.a.bx.1.5		8	11.10	odd	2
4598.2.a.ca.1.5		8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4598 = 2 \cdot 11^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4598.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.912987 q^{3} +1.00000 q^{4} -1.77724 q^{5} +0.912987 q^{6} -5.04753 q^{7} +1.00000 q^{8} -2.16645 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.912987 q^{3} +1.00000 q^{4} -1.77724 q^{5} +0.912987 q^{6} -5.04753 q^{7} +1.00000 q^{8} -2.16645 q^{9} -1.77724 q^{10} +0.912987 q^{12} +5.42371 q^{13} -5.04753 q^{14} -1.62260 q^{15} +1.00000 q^{16} -1.82249 q^{17} -2.16645 q^{18} -1.00000 q^{19} -1.77724 q^{20} -4.60833 q^{21} +5.61764 q^{23} +0.912987 q^{24} -1.84141 q^{25} +5.42371 q^{26} -4.71691 q^{27} -5.04753 q^{28} +2.23982 q^{29} -1.62260 q^{30} +0.386531 q^{31} +1.00000 q^{32} -1.82249 q^{34} +8.97068 q^{35} -2.16645 q^{36} -10.0927 q^{37} -1.00000 q^{38} +4.95177 q^{39} -1.77724 q^{40} +9.28332 q^{41} -4.60833 q^{42} +5.45957 q^{43} +3.85031 q^{45} +5.61764 q^{46} +10.8132 q^{47} +0.912987 q^{48} +18.4776 q^{49} -1.84141 q^{50} -1.66391 q^{51} +5.42371 q^{52} +6.85692 q^{53} -4.71691 q^{54} -5.04753 q^{56} -0.912987 q^{57} +2.23982 q^{58} +3.70481 q^{59} -1.62260 q^{60} +2.89301 q^{61} +0.386531 q^{62} +10.9352 q^{63} +1.00000 q^{64} -9.63923 q^{65} -11.5655 q^{67} -1.82249 q^{68} +5.12883 q^{69} +8.97068 q^{70} -0.872761 q^{71} -2.16645 q^{72} +9.78216 q^{73} -10.0927 q^{74} -1.68119 q^{75} -1.00000 q^{76} +4.95177 q^{78} +9.31807 q^{79} -1.77724 q^{80} +2.19288 q^{81} +9.28332 q^{82} -4.28702 q^{83} -4.60833 q^{84} +3.23901 q^{85} +5.45957 q^{86} +2.04493 q^{87} -5.60537 q^{89} +3.85031 q^{90} -27.3763 q^{91} +5.61764 q^{92} +0.352898 q^{93} +10.8132 q^{94} +1.77724 q^{95} +0.912987 q^{96} -2.90528 q^{97} +18.4776 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9	\( 8 q + 8 q^{2} + 8 q^{4} + 2 q^{5} + 8 q^{7} + 8 q^{8} + 20 q^{9} + 2 q^{10} + 18 q^{13} + 8 q^{14} + 10 q^{15} + 8 q^{16} + 4 q^{17} + 20 q^{18} - 8 q^{19} + 2 q^{20} + 14 q^{21} + 12 q^{23} + 18 q^{26} - 24 q^{27} + 8 q^{28} + 14 q^{29} + 10 q^{30} - 2 q^{31} + 8 q^{32} + 4 q^{34} + 40 q^{35} + 20 q^{36} - 22 q^{37} - 8 q^{38} - 4 q^{39} + 2 q^{40} + 8 q^{41} + 14 q^{42} + 28 q^{43} - 28 q^{45} + 12 q^{46} + 6 q^{47} + 32 q^{49} - 12 q^{51} + 18 q^{52} - 24 q^{53} - 24 q^{54} + 8 q^{56} + 14 q^{58} + 46 q^{59} + 10 q^{60} - 24 q^{61} - 2 q^{62} + 30 q^{63} + 8 q^{64} - 16 q^{65} - 22 q^{67} + 4 q^{68} - 38 q^{69} + 40 q^{70} + 8 q^{71} + 20 q^{72} + 16 q^{73} - 22 q^{74} + 6 q^{75} - 8 q^{76} - 4 q^{78} + 4 q^{79} + 2 q^{80} + 28 q^{81} + 8 q^{82} + 12 q^{83} + 14 q^{84} + 48 q^{85} + 28 q^{86} + 42 q^{87} - 28 q^{89} - 28 q^{90} - 12 q^{91} + 12 q^{92} + 22 q^{93} + 6 q^{94} - 2 q^{95} - 22 q^{97} + 32 q^{98}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^4 + 2 * q^5 + 8 * q^7 + 8 * q^8 + 20 * q^9 + 2 * q^10 + 18 * q^13 + 8 * q^14 + 10 * q^15 + 8 * q^16 + 4 * q^17 + 20 * q^18 - 8 * q^19 + 2 * q^20 + 14 * q^21 + 12 * q^23 + 18 * q^26 - 24 * q^27 + 8 * q^28 + 14 * q^29 + 10 * q^30 - 2 * q^31 + 8 * q^32 + 4 * q^34 + 40 * q^35 + 20 * q^36 - 22 * q^37 - 8 * q^38 - 4 * q^39 + 2 * q^40 + 8 * q^41 + 14 * q^42 + 28 * q^43 - 28 * q^45 + 12 * q^46 + 6 * q^47 + 32 * q^49 - 12 * q^51 + 18 * q^52 - 24 * q^53 - 24 * q^54 + 8 * q^56 + 14 * q^58 + 46 * q^59 + 10 * q^60 - 24 * q^61 - 2 * q^62 + 30 * q^63 + 8 * q^64 - 16 * q^65 - 22 * q^67 + 4 * q^68 - 38 * q^69 + 40 * q^70 + 8 * q^71 + 20 * q^72 + 16 * q^73 - 22 * q^74 + 6 * q^75 - 8 * q^76 - 4 * q^78 + 4 * q^79 + 2 * q^80 + 28 * q^81 + 8 * q^82 + 12 * q^83 + 14 * q^84 + 48 * q^85 + 28 * q^86 + 42 * q^87 - 28 * q^89 - 28 * q^90 - 12 * q^91 + 12 * q^92 + 22 * q^93 + 6 * q^94 - 2 * q^95 - 22 * q^97 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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